What was found
N4KS HAD NORMAL STARTS 1ST, 2 LEGS, NORMAL TAKEOFF PROCEDURE AND PREFLIGHT CHK, OILS CHKD & WALK AROUND DONE. TOOK OFF, CLIMBING THROUGH 12,000 WHEN OIL PSI DROPPED TO 0, BOUNCED BACK TO NORMAL RANGE OF 66-69 A FEW TIMES WITH OIL TEMP SLOWLY RISING BEFORE DROPPING TO 0 CONSTANT WITH POWER IN CLIMB. BURNING ODOR FILLED CABIN & OXYGEN MASK PUT ON BEFORE DECLARING EMERGENCY & REQUESTED DIVERSION TO DPA. LT THROTTLE PULLED BACK TO IDLE IMMEDIATELY & DESCENT REQUESTED. TO ELIMINATE ODOR PILOT MONITORING SWITCHED PRESSURE SOURCE TO RT & PUT COCKPIT RECIRC TO LOW. AFTER DESCENDING THROUGH 6000, ENG OIL PSI & OIL TEMP LEVELED AT 52 & STAYED CONSTANT THROUGH LANDING. AFTER SHUTDOWN & EGRESS, LT ENG EMITTING WHITE SMOKE OUT OF FRONT & HAD AN ODOR FOR 5-10 MINS AFTER SHUTDOWN. POST FLIGHT OIL CHECK SHOWED NO OIL LEFT IN ENG ON THE OIL GAUGE.